兰州大学机构库 >数学与统计学院
时间分数阶扩散方程的源项识别问题
Alternative TitleAn inverse source problem of a time-fractional diffusion equation
李雪莲
Subtype硕士
Thesis Advisor魏婷
2015-05-29
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword源项识别问题 分数阶扩散方程 共轭梯度法 变分问题 唯一性
Abstract本文中,我们考虑一种时间分数阶扩散方程的源项识别问题, 即由部分边界数据来确定未知时间源项. 首先, 我们给出了相应正问题解的存在唯一性和源项识别问题的唯一性结果.其次,由于该问题的不适定性我们引入 Tikhonov 正则化泛函将反问题转化为一个变分问题, 并用共轭梯度法求解该变分问题. 最后我们给出几个数值算例由此证明我们的方法是有效的和稳定的.
Other AbstractThis paper is devoted to identify a time-dependent source term in a time-fractional diffusion equation from boundary solute concentration measurement. The existence and uniqueness for the direct problem with Neumann boundary condition are provided. We propose a variational method to solve the inverse problem and use the conjugate gradient method to solve the optimization problem. We also prove the uniqueness for the inverse source problem. Numerical examples in one-dimension and two-dimension cases are provided to show the effectiveness of the proposed method.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224715
Collection数学与统计学院
Recommended Citation
GB/T 7714
李雪莲. 时间分数阶扩散方程的源项识别问题[D]. 兰州. 兰州大学,2015.
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